Why do we connect a battery to ground when jumping a car?

"Ground" is just a code word which, in this case, refers to the "current return common" circuit node. There is a complete circuit because everything electrical in the car, such as the starter motor, also connects to ground in order to return current to the minus terminal of the battery through the ground. The car's chassis is used for this return network, and so the entire chassis is an extension of the minus terminal of the battery.

During jump-starting, we connect the boosting battery to ground rather than to the dead battery's - terminal for the simple reason that this provides a more direct return path to the good battery which is powering the dead car: the return current does not have to travel through the dead battery's minus terminal hookup cable and then to the jumper cable, but can go directly from the chassis ground to the jumper cable.

A more direct return path allows for better current flow and less voltage drop, like plugging a big appliance directly into an outlet, rather than via an extension cord.

In case you're also wondering why the plus jumper connections are made first, then the minuses. This is because there is no harm done if you leave the minus jumper dangling in the chassis of the car. Anything it accidentally touches is likely to be ground. If you connect both alligator clips on one end before connecting the other end, the other end is now live and you can accidentally touch the clips together to create a short circuit. If you connect the minuses/grounds first and then go to connect one of the pluses, you can create a short circuit, because the opposite side plus is probably dangling and touching something that is grounded.

The - end of the charged battery is already connected to the chassis, the engine, and, particularly, the starter motor. The whole car is designed to work that way. Everything use earth return. All the lights have one wire, and one connection to the chassis. The spark plugs have one wire, and one connection to the engine block. And so on.

OK, on a modern car you use a second wire for the starter motor, because it draws a lot of current and you would get a significant voltage drop and power dissipation in the earth return path. And diesel engines don't have spark plugs. And high power driving lights are driven through a relay like the starter motor is. And lights mounted in plastic fittings need 2 wires.

Given that the -ve end of the battery is connected to the chassis and the shell and the engine, where is the best place to connect the return wire?

Traditionally, you connected it to the chassis or the shell or the engine, so that you didn't have to lean, with a live wire, into the engine compartment, across the engine (hot moving machinery), on to the battery (hydrogen explosion risk, with sulphuric acid as well). But this assumed that the battery was difficult to reach, and that the engine and chassis had a very good connection to the battery (required for the starter motor earth return).

Nowadays, some people make the return connection direct to the battery, if they can reach it easily.

Even if you connect one end of the return wire to the chassis, you normally connect the first end direct to the first battery. This because until the wire is connected to the first battery, it is not a live wire, will not spark when you touch it to something, is not particularly dangerous. After the return wire is connected to the first battery, it is live, and is dangerous. So you connect it to something safe that is easy to reach.

No, you can not connect the return wire to a third car. Cars sit on rubber tires, and the tires insulate each car from other cars. You need a complete circuit from your battery to the other battery.

The main reason for connecting to the positive terminal on the battery first is to do with volatile gases possibly being emitted from the battery. If you connect to both terminals at the battery terminal this will usually cause some kind of spark as you first touch the cable to the terminal, whether you do positive or negative first is irrelevant. Connect the positive at the battery terminal first(no danger of a spark as a complete circuit is not formed), then connect the negative cable to a point on the chassis away from the battery, so the resulting spark is not in the area likely to be affected by any gases. that way you have ruled out the possibility of igniting the gas and have avoided any chance, however small. of an explosion.